Question: $\text D = \left[\begin{array}{rr}5 & -2 \\ -1 & 5\end{array}\right]$ What is the determinant of $\text D$ ?
Solution: The determinant of a 2x2 matrix can be computed the following way: $ \left|\begin{array}{rr}a & b \\ c & d\end{array}\right| = (a \times d)-(b \times c) $ In this specific case, $ \left|\begin{array}{rr}5 & -2 \\ -1 & 5\end{array}\right| = (5 \cdot 5)-(-2 \cdot -1) $ $ = 23 $